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Published on: June 8, 2018
On Low-Rank Multiplicity-Free Complex Fusion Categories
Gert Vercleyen1, Joost Slingerland2
1Department of Mathematics, Purdue University, 150 N University St, West Lafayette, 47907 IN USA.
Abstract:
This paper explains the methods and algorithms we used to obtain explicit F-symbols, R-symbols, and pivotal coefficients of what we believe are all multiplicity-free pivotal complex fusion categories up to rank 7. Particular attention is given to how the individual steps for solving the consistency equations are done with Anyonica, a software package we developed for working with fusion categories. Gauge and automorphism equivalence are reviewed and a method to remove equivalent categories via a gauge-split basis is given. A census of all multiplicity-free fusion categories up to rank 7, along with all compatible braided and pivotal structures, is presented, and comments on their general properties are given.
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